The sample means do not vary as much as the individual values in the population. That the sample means are less variable than the individual values in the population follows directly from the fact that each sample mean averages together all the values in the sample. A population consists of individual outcomes that can take on a wide range of values, from extremely small to extremely large. However, if a sample contains an extreme value, although this value will have an effect on the sample mean, the effect is reduced because the value is averaged with all the other values in the sample. As the sample size increases, the effect of a single extreme value becomes smaller because it is averaged with more values.
(Excerpt from my stat book)
I find this contradictory because they said that a sample mean averages together all values in the sample, but a population mean also averages together all the values. Also, they said that an extreme value's effect will be reduced when the sample size increases as it is averaged with more values. But in that case, since the population has the widest range doesn't the same thing apply even more?
So, why is the sample mean's standard deviation less than that of the population?